%% Original template: bare_jrnl.tex
%% V1.3
%% 2007/01/11
%% by Michael Shell

\documentclass[journal]{IEEEtran}
\usepackage{pgf}
\usepackage{tikz}
\usepackage[cmex10]{amsmath}
%\usepackage[caption=false]{caption}

\begin{document}
% paper title
% can use linebreaks \\ within to get better formatting as desired
\title{Patch Antenna Design}

% use \thanks{} to gain access to the first footnote area

\author{ Attique Dawood 
\thanks{ Attique Dawood is an Instructor at FAST-NU, Islamabad}}% <-this % stops a space

\markboth{fast-emrc, December 14, 2011}%
{Dawood : Patch Antenna Design}

\maketitle

\begin{abstract}
%\boldmath
Resonant frequency of a rectangular patch antenna is dependent on dimensions of the patch and permittivity of substrate.
\end{abstract}

\begin{IEEEkeywords}
Antenna, patch.
\end{IEEEkeywords}

\section{Introduction}
% The very first letter is a 2 line initial drop letter followed
% by the rest of the first word in caps.
\IEEEPARstart{T}{his} paper demonstrates how a patch antenna can be designed at a particular frequency by
varying dimensions of the patch and permittivity of substrate.
% You must have at least 2 lines in the paragraph with the drop letter

\section{Geometry of Patch Antenna}
A rectangular patch on a substrate with ground plane underneath is the simplest form of a patch antenna.
The dimensions of patch are $L$ and $W$ and $h$ is the substrate height. $\epsilon_r$ is the relative permittivity
of the substrate.
\newline

\begin{figure}[here]
\centering
\begin{tikzpicture}
	\def\x{3cm};

	% Ground plane
	\filldraw (-\x,0cm) rectangle (\x,-0.05cm);
	% Substrate
	\filldraw[gray] (-\x+0.5cm,0cm) rectangle (\x-0.5cm,0.2cm);
	% Patch
	\filldraw (-\x+1.5cm,0.2cm) rectangle (\x-1.5cm,0.25cm);

	\coordinate [label=right:Patch] (PatchLabel) at (1,1);
	\draw (0,0.25) -- (PatchLabel);

	\coordinate [label=right:Substrate] (SubstrateLabel) at (\x,0.5cm);
	\draw (\x-0.5cm,0.2cm) -- (SubstrateLabel);

	\coordinate [label=right:Ground Plane] (GroundPlaneLabel) at (\x-1cm,-0.5cm);
	\draw (1,-0.05) -- (GroundPlaneLabel);
	
	\draw [very thin, <->] (-\x+0.4cm, 0cm) -- (-\x+0.4cm,0.2cm);
	\coordinate [label=left:$h$] (hLabel) at (-\x+0.4cm,0.3cm);

\end{tikzpicture}
\caption{Side view of patch antenna}
\label{Patch_Antenna_Side_View}
\end{figure}

\begin{figure}[here]
\centering
\begin{tikzpicture}
	\def\x{5cm};

	% Substrate
	\filldraw[gray] (0cm,0cm) rectangle (\x,\x);
	% Patch
	\filldraw (1.3cm,1.5cm) rectangle (\x-1.3cm,\x-1.5cm);
	% Feed
	\filldraw (0cm,\x/2-0.2cm) rectangle (1.3cm,\x/2+0.2cm);

	\draw [|<->|] (1.3cm, \x-1.3cm) -- (\x-1.3cm,\x-1.3cm);
	\coordinate [label=above:$L$] (LLabel) at (\x/2,\x-1.3cm);

	\draw [|<->|] (\x-1.1cm, 1.5cm) -- (\x-1.1cm,\x-1.5cm);
	\coordinate [label=right:$W$] (WLabel) at (\x-1.1cm,\x/2);

	\coordinate [label=below:Patch] (PatchLabel) at (1cm,1cm);
	\draw (2cm,2cm) -- (PatchLabel);

	\coordinate [label=above:Feed] (FeedLabel) at (0.6cm,\x/2+0.5cm);
	\draw (0.6cm,\x/2+0.2cm) -- (FeedLabel);
	
	\coordinate [label=right:Substrate] (SubstrateLabel) at (\x-2cm,0.5cm);


\end{tikzpicture}
\caption{Geometry of patch antenna}
\label{Patch_Antenna_Geometry}
\end{figure}

\section{Design Procedure}
To design patch at a particular resonant frequency ($f_r$), $h$
and $\epsilon_r$ of substrate are specified. From these,
$W$ and $L$ are calculated.

\subsection{Design Equations}
Following equations~\cite{miranda} outline a procedure to calculate values of $W$ and $L$:

\begin{equation}
	W=\dfrac{c}{2f_r}\left(\dfrac{\epsilon_r+1}{2}\right)^{-1/2}
	\label{W:formula}
\end{equation}
\begin{equation}
	\epsilon_{\mathrm{eff}}=\dfrac{\epsilon_r+1}{2}+\dfrac{\epsilon_r-1}{2}\left[1+\dfrac{12h}{W}\right]^{-1/2}
	\label{eeff:formula}
\end{equation}
% \mathrm{...} removes the math font from anything written inside. We need 'eff' to be of normal type.
\begin{equation}
	\Delta l=0.412h\left(\dfrac{\epsilon_{\mathrm{eff}}+0.3}{\epsilon_{\mathrm{eff}}-0.258}\right) \left(\dfrac{W/h+0.264}{W/h+0.8}\right)
	\label{Delta l:formula}
\end{equation}
\begin{equation}
	L=\dfrac{c}{2f_r\sqrt{\epsilon_{\mathrm{eff}}}}-2\Delta l
	\label{L:formula}
\end{equation}
\\
\section{Patch Antenna Design at 3 GHz}
In order to design a patch antenna operating at 3 GHz with
$\epsilon_r=2.2$ and $h=3$mm, values of $L$ and $W$ were
computed as $31.94$mm and $39.53$mm. A simulation was performed
using Ansoft's finite element based simulation software HFSS.
$S_\mathrm{{11}}$ plotted against frequency is given in figure 3.

% .png format does not work with latex. If youŕe using latex, then use .eps format.
\begin{figure}[here]
\centering
\includegraphics[scale=0.28]{PatchHFSS}
\caption{$S_{\mathrm{11}}$ vs frequency for patch antenna at 3GHz}
\end{figure}

\section{Conclusion}
This paper demonstrates how a simple rectangular patch antenna at
a particular resonant frequency can be designed. Simulated results
show close resemblance to the predicted values.

% use section* for acknowledgement
\section*{Acknowledgment}

The author would like to thank the EMRC members for their support and cooperation.

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\begin{thebibliography}{2}

\bibitem{miranda}
H.~Miranda, \emph{Patch Antenna Design}, Stanford lecture slides, 2007.

\bibitem{emtalk}
http://www.emtalk.com

\end{thebibliography}

\begin{IEEEbiography}{Attique Dawood}
did his BS from FAST, Islamabd in 2006. He is currently
working as an instructor and part of the EMRG group at FAST, Islamabad.
\end{IEEEbiography}

\end{document}


